A mathematical model for Babesiosis disease in bovine and tick populations

Aranda, Diego; Trejos, Deccy Y.; Valverde, Jose C.; Micó, Rafael Jacinto Villanueva

doi:10.1002/mma.1544

Cited by 19 publications

(61 citation statements)

References 8 publications

(11 reference statements)

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“…In this section, we establish a discrete-time model for the dynamics of the evolution of the Babesiosis disease in bovine and tick populations, considering the same influencing parameters as in the continuous-time model proposed in [6].…”

Section: Mathematical Modelmentioning

confidence: 99%

“…After that, in view of this previous one, a model of partial differential equations for Babesia bovis was formulated by Friedman and Yakubu [7]. Besides, based on our work in [6], Carvalho et al [8] presented a new version of our classical model changing the ordinary derivative by fractional Caputo derivate. Likewise, in [9], authors study a fractional-order scheme model on the disease.…”

Section: Introductionmentioning

confidence: 97%

“…In [6], we introduced a model based on ordinary differential equations for bovine Babesiosis caused by Babesia bigemina and Babesia bovis for the first time. After that, in view of this previous one, a model of partial differential equations for Babesia bovis was formulated by Friedman and Yakubu [7].…”

Section: Introductionmentioning

confidence: 99%

“…Likewise, in [9], authors study a fractional-order scheme model on the disease. Our continuous model in [6] has also served as a basis to set out and study similar models, including other factors such as a two-stage in the cattle class in [10] or the effect of seasonal changes in [11]. Moreover, in [12] a study of the dynamic behavior of our model is performed using a multistage modified sinc method which is a computational algorithm for approximating solutions of the classical system in a sequence of (time) intervals.…”

Section: Introductionmentioning

confidence: 99%

“…As said in [13], discretization of continuous-time models is an interesting and prominent trend. Following this idea, in the present work, we deal with a discrete-time version of the classical model for bovine Babesiosis proposed in [6]. In fact, discretization of classical continuous models could help to check the skill in the selection of the factors to the design of the model.…”

Section: Introductionmentioning

confidence: 99%

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A discrete epidemic model for bovine Babesiosis disease and tick populations

Aranda¹,

Trejos²,

Valverde³

2017

Open Physics

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Abstract:In this paper, we provide and study a discrete model for the transmission of Babesiosis disease in bovine and tick populations. This model supposes a discretization of the continuous-time model developed by us previously. The results, here obtained by discrete methods as opposed to continuous ones, show that similar conclusions can be obtained for the discrete model subject to the assumption of some parametric constraints which were not necessary in the continuous case. We prove that these parametric constraints are not artificial and, in fact, they can be deduced from the biological significance of the model. Finally, some numerical simulations are given to validate the model and verify our theoretical study.

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A discrete epidemic model for bovine Babesiosis disease and tick populations

Aranda¹,

Trejos²,

Valverde³

2017

Open Physics

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Stability and bifurcation in epidemic models describing the transmission of toxoplasmosis in human and cat populations

Ferreira

Echeverry

Peña

2017

Math Methods in App Sciences

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A five-dimensional ordinary differential equation model describing the transmission of Toxoplamosis gondii disease between human and cat populations is studied in this paper. Self-diffusion modeling the spatial dynamics of the T. gondii disease is incorporated in the ordinary differential equation model. The normalized version of both models where the unknown functions are the proportions of the susceptible, infected, and controlled individuals in the total population are analyzed. The main results presented herein are that the ODE model undergoes a trans-critical bifurcation, the system has no periodic orbits inside the positive octant, and the endemic equilibrium is globally asymptotically stable when we restrict the model to inside of the first octant. Furthermore, a local linear stability analysis for the spatially homogeneous equilibrium points of the reaction diffusion model is carried out, and the global stability of both the disease-free and endemic equilibria are established for the reaction-diffusion system when restricted to inside of the first octant. Finally, numerical simulations are provided to support our theoretical results and to predict some scenarios about the spread of the disease.

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Feedback control variables to restrain the Babesiosis disease

Dang

Hoang

Trejos

et al. 2019

Math Methods in App Sciences

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In this paper, we complete the study of the dynamics of a recognized continuous-time model for the Babesiosis disease. The local and global asymptotic stability of the endemic state are established theoretically and experimentally. In addition, to restrain the disease in the original model when the endemic state exists, we propose and study the continuous model with feedback controls.The global stability of the boundary-equilibrium point of this model is analyzed by means of rigorous mathematical methods. As an important consequence of this result, we propose a strategy to select feedback control variables in order to restrain the disease in the original model. This strategy allows us to make the disease vanish completely. In other words, the feedback controls are specially effective for restraining disease in the model. The validity of the established theoretical result is supported by a set of numerical simulations. KEYWORDS attractors, Babesiosis disease, feedback control, global stability, Lyapunov functions and stability, numerical treatment of dynamical systems MSC CLASSIFICATION 34D23; 37B25; 93B52 Math Meth Appl Sci. 2019;42:7517-7527.wileyonlinelibrary.com/journal/mma

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A mathematical model for Babesiosis disease in bovine and tick populations

Cited by 19 publications

References 8 publications

A discrete epidemic model for bovine Babesiosis disease and tick populations

A discrete epidemic model for bovine Babesiosis disease and tick populations

Stability and bifurcation in epidemic models describing the transmission of toxoplasmosis in human and cat populations

Feedback control variables to restrain the Babesiosis disease

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